There are good guy characters to identify with:
- Peter Russo (if you don't mind his alcoholism and whoring around)
- Lucas Goodwin
- Zoe Barnes (I couldn't stand her but she's narratively a good guy)
- Tom Hammerschmidt (starts off unlikeable, but gets redeemed in the last seasons)
- Cathy Durant
- Seth Grayson (arguably, because he's not aware of truly immoral dealings)
I could've extended this list further, but I'm afraid that this will lead to spoilery implications.
The thing with House of Cards is that its central character is a bad guy. Without spoiling the ongoing plot, House of Cards has (so far) been a story where the bad guy manages to overcome the good guys time and time again.
Instead of the good guy facing a different bad guy every season, this is more a matter of the same bad guy facing a different good guy every season.
About your comparison to Designated Survivor.
Both House of Cards and Designated Survivor mainly focus on the same philosophy:
United we stand, divided we fall.
But they explore the philosophy from a different point of view.
United, we stand.
Designated Survivor showcases that a united country can overcome the biggest hardships. The characters are tackling a shared goal/problem, and their teamwork causes them to succeed.
Divided, we fall.
House of Cards, however, showcases that a divided government is a problem. The politicians in House of Cards are tackling each other, instead of tackling a shared goal/problem. The lack of teamwork perpetuates a broken system.
Edit - Slight elaboration:
In the last few years, we've seen more shows where the classic good/bad archetypes get subverted.
Breaking Bad and Better Call Saul are really good examples of this. The shows explore criminal environments. Most characters are a professional criminal in one way or another. However, most of them have relatable backstories, which humanizes them:
(note that I'm not avoiding spoilers since the question isn't about Breaking Bad)
- Walter White begins his life of crime with the intention of keeping his family safe when he's gone.
- Jesse Pinkman gets treated like a worse person than he is (by his parents), which contributes to why he ended up in this life. He has never shown any immoral behavior except his opinion that drugs should be freely useable. He very much wants children to be happy and safe, and abhors murder (the only to this exception was when he killed child murderers)
- Jimmy McGill/Saul Goodman breaks the rules but usually in a way where he tries to do good, or at least to make something happen that Jimmy thinks is just (like Kim getting Mesa Verde as a client).
- Mike Ehrmantraut was a dirty cop, but his son's death was a moral wake up call for him. He takes shady jobs but avoids killing anyone, even refuses to take a gun unless he's expecting an unavoidable shootout.
- Gus Fring started a (drug) business with a lifelong friend. The lifelong friend was killed, and Gus ended up with a violent cartel that he couldn't walk away from. Gus is stuck with the cartel, as much as Walt was stuck with Gus.
The show very much explores that not everyone who commits crimes is necessarily a villain, or intends to do evil.
Bring it back to House of Cards, Doug Stamper is a good example of such a relatable bad guy. Avoiding spoilers, Doug's character is composed of traits that are usually found in a narrative hero:
- He has an undying loyalty for his best friend.
- He hardly ever slacks off or phones it in. He does what needs to be done.
- He struggles with personal issues that torment him every day.
- He wants someone to love.
However, these "good guy traits" eventually get soured.
- His best friend is a villain.
- He never refuses a task based on it being immoral. He never even questions having to commit felonies.
- Every romantic engagement he's had ended up in a very creepy spot.
So it's up to you to decide whether you consider Doug evil (based on his actions) or good (based on his intentions and general approach to life).
I think most fans of the show would agree that if Doug had been loyal to a good guy, he would've been a good guy himself. So then the question becomes whether we should condemn Doug because he's loyal to a friend who has sent Doug down the immoral path?